The answer is E; neither statement is at all helpful. Taking the question literally, we need to find the range (i.e. largest - smallest) of the set of values which are greater than M -4 and less than M + 4, where M is the mean. It's clear that the range is no larger than 8, but you can't assume that the range is in fact 8. Take, for example, the following data set:
\{ -2\sqrt{10}, 0, 0, 0, 2\sqrt{10} \}The standard deviation of this set is 4, and the set of values within one standard deviation of the mean is simply {0,0,0}, which has a range of 0.
I'd guess the question designer intended to ask something different with this question. If the 'correct' answer is B, I'd guess that the question designer meant 'range' in the colloquial sense (the question might be trying to say: values within one s.d. of the mean must lie between which min and max values?), and not the sense in which the word is used on the GMAT or in real statistics (largest-smallest). If that's the intended meaning, it's a badly written question, and you would never encounter such ambiguity on the real test. What is the source?
_________________
Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.
Private GMAT Tutor based in Toronto
close
